Determining Temperature Profiles in the Extruder during the Material Extrusion of an Amorphous Polymer Using Two Coupled Physics-Informed Neural Networks

Determining Temperature Profiles in the Extruder during the Material Extrusion of an Amorphous Polymer Using Two Coupled Physics-Informed Neural Networks | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Determining Temperature Profiles in the Extruder during the Material Extrusion of an Amorphous Polymer Using Two Coupled Physics-Informed Neural Networks Cheng Luo This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-6938823/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 08 Jan, 2026 Read the published version in Progress in Additive Manufacturing → Version 1 posted You are reading this latest preprint version Abstract There is no exact analytical solution for the heat-transfer problem in the extruder of material extrusion additive manufacturing, except for approximate solutions to simplified cases. Physics-informed neural networks (PINNs) are machine learning models that use artificial neural networks to numerically solve problems based on underlying physical laws. In this work, two coupled PINNs are developed to solve the heat-transfer problem without simplifying the governing equations or interface conditions. The goal is to accurately determine the temperature profiles inside the extruder, focusing specifically on the extrusion of amorphous polymers. To validate the approach, the two PINNs are first applied separately to solve simpler heat-transfer problems. They are then combined to solve the full heat-transfer problem. The PINN solution is compared with the approximate solutions to simplified cases for extruding acrylonitrile butadiene styrene (ABS). The Python implementation runs in under 10 min on an online platform, demonstrating practical usability. The developed PINN model provides a simple and efficient method for determining temperature profiles in the extruder during the extrusion of various amorphous materials, delivering critical information for optimizing the MatEx process. Material extrusion Thermal model Physics-informed neural network Non-Newtonian fluid Temperature-dependent viscosity Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Published Journal Publication published 08 Jan, 2026 Read the published version in Progress in Additive Manufacturing → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-6938823","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":484423104,"identity":"4fa984a4-0fce-4b33-ad0b-021ffd084eb3","order_by":0,"name":"Cheng Luo","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAw0lEQVRIiWNgGAWjYDACCRBRwMDAD+EyE6vFgIFBsoGZVC0GB4jVwj+7+djDLwaH5Yxv5B/8wFBhndhA0JI7x9KNZQwOG5vdSGaWYDiTTliLgUSOmbSEweHEbTeSGSQY2w4ToyX/G1jL5hnJzD8Y/xGlJYdN8gNQywaJZDYJxgYitEjcSDOTZjBIN5Y489jMIgHoMYJa+GckP5P8UWEtx9+e+PjGhxprWYJaQICZB8ZKIEY5CDD+IFblKBgFo2AUjEwAAIZMOk7THRNaAAAAAElFTkSuQmCC","orcid":"","institution":"The University of Texas at Arlington","correspondingAuthor":true,"prefix":"","firstName":"Cheng","middleName":"","lastName":"Luo","suffix":""}],"badges":[],"createdAt":"2025-06-20 12:23:09","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-6938823/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-6938823/v1","draftVersion":[],"editorialEvents":[{"content":"https://doi.org/10.1007/s40964-025-01488-5","type":"published","date":"2026-01-08T15:57:38+00:00"}],"editorialNote":"","failedWorkflow":false,"files":[{"id":100069221,"identity":"0dbf1d52-fe6c-419a-bb4c-03cf2161ad26","added_by":"auto","created_at":"2026-01-12 16:11:25","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":878238,"visible":true,"origin":"","legend":"","description":"","filename":"PINNsforheattransferinMatExPIAMblindedcopy.pdf","url":"https://assets-eu.researchsquare.com/files/rs-6938823/v1_covered_9358cb85-1c86-49ad-b84b-6a750dca613d.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Determining Temperature Profiles in the Extruder during the Material Extrusion of an Amorphous Polymer Using Two Coupled Physics-Informed Neural Networks","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":true,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Material extrusion, Thermal model, Physics-informed neural network, Non-Newtonian fluid, Temperature-dependent viscosity","lastPublishedDoi":"10.21203/rs.3.rs-6938823/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-6938823/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eThere is no exact analytical solution for the heat-transfer problem in the extruder of material extrusion additive manufacturing, except for approximate solutions to simplified cases. 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